How to remove/blur the texture seam?
You have to use a higher resolution texture (256X256 is really small) and hide the seams using texture paint brushes. Here's the result which uses the higher resolution texture and corrective brushes.


To get rid of the seam use a Clone brush in a Texture Paint mode. Press Ctrl+LMB to place the cursor in the area you want to clone and then LMB to paint.


Use a Smear brush to blur the texture and hide the seams/imperfections.


NOTE: Don't forget to save your painted texture in the UV Editor!

Here's the corrected .blend: